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LOW COMPLEXITY RANDOM NUMBER GENERATOR FOR CRYPTOGRAPHIC KEYS IN A WIRELESS COMMUNICATION ENVIRONMENT

Publishing Venue

Motorola

Related People

Authors:

David B. Taubenheim•Dr. Brian T. Kelley

Abstract

Wireless communication products are growing ever more popular and have become a necessity for many people. However, one difficulty frequently arising in communications and computing is the generation of random numbers for encryption keys and authentication [ 1 J. This paper introduces an ele- gant, yet simple hardware random number generator (RNG) that yields statistically unbiased random numbers [2][6][8]. By utilizing existing structures commonly encountered in wireless data devices, the approach is extremely low in complexity and does not require additional special purpose analog struc- tures, completely symmetric digital structures [8], or additional memory or digital logic [7].

Copyright

Motorola Inc. September 1999

Country

United States

Language

English (United States)

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Page 1 of 3

Developments Technical 0 M MO-LA

LOW COMPLEXITY RANDOM NUMBER GENERATOR

FOR CRYPTOGRAPHIC KEYS IN A WIRELESS COMMUNICATION ENVIRONMENT

by David 8. Taubenheim and Dr. Brian T. Kelley

INTRODUCTION

Wireless communication products are growing ever more popular and have become a necessity for many people. However, one difficulty frequently arising in communications and computing is the generation of random numbers for encryption keys and authentication [ 1 J. This paper introduces an ele- gant, yet simple hardware random number generator (RNG) that yields statistically unbiased random numbers [2][6][8]. By utilizing existing structures commonly encountered in wireless data devices, the approach is extremely low in complexity and does not require additional special purpose analog struc- tures, completely symmetric digital structures [8], or additional memory or digital logic [7].

METHOD

We illustrate a typical digital superheterodyne transceiver as the basis for this RNG. After RF down-conversion in the analog portion of the trans- ceiver (Figure l), a digital signal processing (DSP) block demodulates the signal further. The resulting baseband data symbols arc interpreted by a (com- munications) protocol decoder, typically consisting of a microprocessor or an application-specific inte- grated circuit. During an intermediate stage of the DSP block, the sampled signal is mixed with ei@n, resulting in in-phase (I) and quadrature (Q) base-

band components of the signal. Random numbers are produced by selecting the least significant bits (LSBs) of the 16-bit I and Q data samples.

Each stage of the receiver contributes a separate noise component to the desired signal. The specific receiver prototyped in our design, as illustrated in Figure 1, was determined to add approximately 3 dB of noise to the desired signal. When the signal arrives at the ADC, the sampling process contributes additional noise components. The useful dynamic range of the ADC is a measure of the weakest signal it can sample accurately and is also expressed in dB. For the ADC used in this digital transceiver proto- type, the useful dynamic range is 85 dB. Thus. sig- nals 85 dB weaker than the strongest signal the ADC are indistinguishable from noise. The ADC quantizes data to approximately 14.1 digital bits (i.e. 20 * log 2'4.').

Inside the DSP block, each sample from the ADC is converted to 16-bit representation. However, the dynamic range of a 16.bit word is 2O*log 216 (i.e. 96 dB). It is critical to note that a 16-bit word contains about 11 dB more useful dynamic range, or 1.8 bits more, than the ADC. Therefore, the LSB of the 16-bit sample, which falls under the noise floor, is uncertain. This constitutes a random process whose random qualities we will examine next.